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9.5: COMPLETING THE SQUARE:

Factoring: A process used to break down any polynomial into simpler polynomials. 9.5: COMPLETING THE SQUARE:. Zero-Product Property: For any real numbers a and b, If a b = 0 Then a = 0 or b = 0.

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9.5: COMPLETING THE SQUARE:

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  1. Factoring: A process used to break down any polynomial into simpler polynomials. 9.5: COMPLETING THE SQUARE: Zero-Product Property: For any real numbers a and b, If ab= 0 Then a= 0 or b = 0. Complete the square: A process where x2+bx can be changed into a perfect-square trinomial by adding

  2. Procedure: 1) Find the values of a and b. COMPLETE THE SQUARE: ax2 + bx 2) Use the formula of and add it to ax2+ bx. 3) Re-write ax2+ bx+ as a product of perfect squares.

  3. GOAL:

  4. COMPLETE THE SQUARE: Ex: What integer is needed to complete the square: x2+5x+ ___?

  5. SOLUTION: Following the steps given 1) a = 1 and b = 5 2)   (2.5)  x2+5x+ (2.5) 3) x2+5x+6.25  (x+2.5)(x+2.5)  (x+2.5)

  6. FINDING THE SOLUTION: (x+2.5)= 0 Using the Zero-Product property (x+2.5)= 0 (x+2.5) = 0 X = -2.5 The solutions are x = -2.5 twice. If something happens twicewe only touch the x-axis at that point.

  7. COMPLETING THE SQUARE: ax2 + bx = C Ex: What is the solutions of the equation: x2+6X=216

  8. SOLUTION: x2+6X=216 1) a = 1 and b = 6 2)   (3)  x2+6x+(3)=216+(3) 3) x2+6x+9  (x+3)(x+3)  (x+3)= 225  (x+3)=  x = -3  x = -8, 2.

  9. YOU TRY IT: Ex: What are the solutions of: r2-4r=30

  10. SOLUTION: R2-4r=30 1) a = 1 and b = -4 2)   (-2)  x2-4x+(-2)=30+(-2) 3) x2-4x+4  (x-2)(x-2)  (x-2)= 34  (x-2)= x = 2  x = -3.8 and 7.8

  11. REAL-WORLD: You are planting A flower garden Consisting of 3 Square plots Surrounded by 1 ft border. The total area of the garden and the border is 100tf2. What is the side length x of each square plot?

  12. SOLUTION: Adding an x to both sides of the picture we get: x +2 3x +2 A = b h A = (x +2)(3x +2) 100= (x +2)(3x +2)  FOIL 100= 3x2+ 8x + 4

  13. To complete the square we now put it in the ax2+bx = c form: SOLUTION: 100= 3x2+ 8x + 4 3x2+ 8x = 100 - 4 3x2+ 8x = 96 We always prefer a to be 1, so divide by 3: x2+ x =

  14. SOLUTION: Continue 1) x2+ x = Now a = 1 , b = 2)    3) x2+ x+ = + (x + )(x+ )= +

  15. VIDEOS: SOLVING BY FACTORING Solving by factoring: http://www.khanacademy.org/math/algebra/quadratics/factoring_quadratics/v/Example%201:%20Solving%20a%20quadratic%20equation%20by%20factoring

  16. VIDEOS: SOLVING BY FACTORING Solving by factoring: http://www.khanacademy.org/math/algebra/quadratics/factoring_quadratics/v/Example%202:%20Solving%20a%20quadratic%20equation%20by%20factoring http://www.khanacademy.org/math/trigonometry/polynomial_and_rational/quad_formula_tutorial/v/solving-quadratic-equations-by-completing-the-square

  17. CLASSWORK:Page 508-509: Problems: 4, 7, 15, 21, 25, 36, 37.

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